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A218836 Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array. 10

%I #29 Mar 09 2023 17:33:17

%S 1,2,7,21,65,200,616,1897,5842,17991,55405,170625,525456,1618192,

%T 4983377,15346786,47261895,145547525,448227521,1380359512,4250949112,

%U 13091204281,40315615410,124155792775,382349636061,1177482265857,3626169232672,11167134898976

%N Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.

%H R. H. Hardin, <a href="/A218836/b218836.txt">Table of n, a(n) for n = 0..210</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,1).

%F a(n) = 2*a(n-1) +3*a(n-2) +a(n-3).

%F G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1- x*(4*k+2 +3*x+x^2)/(x*(4*k+4 +3*x+x^2) + 1/Q(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Oct 04 2013

%F G.f.: 1/(1-2*x-3*x^2-x^3). - _Alois P. Heinz_, Apr 21 2020

%e Some solutions for n=3

%e ..1..1....1..1....0..0....1..0....0..0....1..0....0..0....1..1....0..0....1..0

%e ..1..1....1..1....0..1....0..1....0..0....0..0....0..0....0..0....0..1....0..0

%e ..1..1....0..0....0..0....1..1....0..1....1..1....1..1....1..1....1..1....0..1

%p a:= n-> (<<0|1|0>, <0|0|1>, <1|3|2>>^n. <<1, 2, 7>>)[1$2]:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Apr 21 2020

%Y Column 2 of A218842.

%K nonn,easy

%O 0,2

%A _R. H. Hardin_, Nov 07 2012

%E a(0)=1 prepended and first g.f. adapted by _Alois P. Heinz_, Apr 21 2020

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)